Post on 21-Apr-2015
Kinetics of Microbial Growth
Yield Coefficient, Y
• Part of substrate goes to cell material production. Part goes to energy production.
• Substrate consumption often measured as BOD
• Can be computed from stoichiometrics or energetics for single compounds
• Measured in laboratory for complex mixtures• Aerobic Y typically 0.3 to 0.5.• “Synthesis” or “true” vs. “Observed” yield
consumedsubstrateofMass
producedmaterialcellofMassY =
Substrate Consumption
• Object of biological wastewater treatment
• Rate of consumption, dS/dt = rsu
• Michaelis-Mentenexpression
• Consequence of enzyme-substrate reaction kinetics
( )127.EqSK
kXS-r
ssu −
+=
Substrate conc. decreasing
PESESE +→+↔+
“Half Velocity” or M-M constant
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30 35 40 45 50
Substrate Concentration
Su
bst
rate
Uti
liza
tio
n R
ate,
-r
su
Asmyptote
S >> Ks-rsu ≈ kX= 660 mg/L-d
Ks >> S
-rsu ≈ (S)kX/Ks
≈ k’S
Ks= 5
( )127.EqSK
kXS-r
ssu −
+=
After M&E Figure 7-11:k = 6.6 mg COD/mg VSSX = 100 mg VSS/LKs= 5 mg COD/L
660
330
k’
1
Bacterial Growth
• Consequence of biological wastewater treatment
• Rate of growth, dX/dt = rg
• Max specific growth rate = µm (=rgm/X)• Related to substrate consumption by Y• Substitute 7-14 into 7-12: ( )
( )147.EqY
k
137.EqkY
m
m
−µ=
−=µ
( ) ( )157.EqSKY
XS-r
s
msu −
+µ=
Microbial Growth
• rg also related to rsuby Y→rg = -Yrsu
• Endogenous decay→Cell material
consumed for maintenance energy
→Cell death and predation
→rd = kdX
• Therefore: ( )217.EqXkYrr dsug −−−=
Microbial Growth
( )217.EqXkYrr dsug −−−=
( )227.EqXkSK
kXSYr d
sg −−
+=
( )127.EqSK
kXS-r
ssu −
+=Substitute
Substitute
( )"a"227.EqXkSK
XSr d
s
mg −−
+µ=
( )147.EqY
k m −µ=
Specific Growth Rate, µgr
Xµ =
( )227.EqXkSK
kXSYr d
sg −−
+=
( )237.EqkSK
kSY d
s
−−+
=µ
Substitute into
Or substitute into ( )"a"227.EqXkSK
XSr d
s
mg −−
+µ=
( )a237.EqkSK
Sd
s
m −−+
µ=µ